Finite Group Databasebeta

← #25080351

Subgroups — #25080351

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145567C211yesmaximal, characteristic
2#19145314C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134165C211yesmaximal, characteristic, complemented
5#19134147C211yesmaximal, characteristic, complemented
6#19134106C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134034C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19133987C211yesmaximal, characteristic, complemented
11#19133945C211yesmaximal, characteristic, complemented
12#19133345C211yesmaximal, characteristic, complemented
13#19133260C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583281—21no—
19#14583273C2211yescharacteristic
20#14583256—21no—
21#14583249C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583147—21no—
24#14583147—21no—
25#14583109C2211yescharacteristic
26#14583104C2211yescharacteristic
27#14583099C2211yescharacteristic
28#14583094C2211yescharacteristic
29#14583059—21no—
30#14583042—21no—
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582997—21no—
34#14582997—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582971—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#479—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#465—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74C2×#10621877—21no—
75C2×#10621877D411yescharacteristic
76C2×#10621877D411yescharacteristic
77C22×C43⋊C8—21no—
78#13063325C2311yescharacteristic
79#13063322C2311yescharacteristic
80#13063313—21no—
81#13063299—21no—
82#13063299—21no—
83C4×D172—21no—
84C4×D172—21no—
85#13063258—21no—
86#13063258—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063248—21no—
96#13063248—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236D411yescharacteristic
107#13063236D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C22×C8×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#102×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×C22⋊D43—41no—
154#10621898—81no—
155#10621898—81no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161Q16×C43—81no—
162SD16×C43—81no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43#4111yescharacteristic
189C42×C43C2411yescharacteristic
190#10621885—81no—
191#10621884—42no—
192#10621884—42no—
193#10621884—81no—
194#10621883—81no—
195#10621882—81no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200#10621877—22no—
201#10621877—41no—
202#10621877—42no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—42no—
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211C2×C43⋊C8C2×D411yescharacteristic
212C23×C43—21no—
213C23×C43#12111yescharacteristic
214C22×D43—41no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—81no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C22⋊D43—82no—
243C2×Dic43—41no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—41no—
248D172—81no—
249C4×D43—82no—
250Dic86—41no—
251Dic86—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261C43⋊C8#13512yes—
262#19252—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43C2×#12111yescharacteristic
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43—41no—
280C4×C43—81no—
281C4×C43—81no—
282C4×C43C2×#13511yescharacteristic
283C4×C43#57511yescharacteristic
284C4×C43#57611yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—81no—
287#3248D4311yescharacteristic, complemented
288#3212—431no—
289#3182—431no—
290#2969—431no—
291#1702—431no—
292#1700—431no—
293#1693—431no—
294#1685—431no—
295#1681—431no—
296#1679—431no—
297#1674—431no—
298#1666—431no—
299#1565—431no—
300#1544—431no—
301#1540—431no—
302C2×C43—41no—
303C2×C43—81no—
304C2×C43#303511yescharacteristic
305C2×C43#306211yescharacteristic
306C2×C43#306911yescharacteristic
307D43—161no—
308#533C2×D4311yescharacteristic
309#532—431no—
310#529C2×D4311yescharacteristic
311#500—431no—
312#495—861no—
313#492—431no—
314#488—861no—
315#487—431no—
316#486—431no—
317#479—21no—
318#475C2×D4311yescharacteristic
319#474C2×D4311yescharacteristic
320#468—861no—
321#468—861no—
322#467—21no—
323#465—21no—
324#464—21no—
325#462—431no—
326#462C2×D4311yescharacteristic
327#461—431no—
328#461C2×D4311yescharacteristic
329#460—431no—
330#459—431no—
331#452—861no—
332#449—861no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336#440—861no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#431—431no—
343#431—431no—
344C2×C4⋊C8C2×D4311yescharacteristic
345#405—861no—
346C4×M16—431no—
347#335—431no—
348#335—431no—
349#334—431no—
350#334—431no—
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#331—431no—
358#331—431no—
359C43#1925211yescharacteristic, complemented, Sylow
360C2×#41—861no—
361C2×Q16—21no—
362C2×Q16—861no—
363C2×SD16—21no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—861no—
369C2×M16—431no—
370C2×M16—431no—
371C2×M16—861no—
372C22×C8—21no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8C22×D4311yescharacteristic
376C4⋊Q8C22×D4311yescharacteristic
377#127—431no—
378#126—21no—
379#125—21no—
380#125C22⋊D4311yescharacteristic
381#124—861no—
382#124C22⋊D4311yescharacteristic
383#123—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8C22⋊D4311yescharacteristic
387#121—861no—
388#121—861no—
389#121C22⋊D4311yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C22×D4311yescharacteristic
393C4×D4—21no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4C22×D4311yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C22×D4311yescharacteristic
400#107—21no—
401#107—861no—
402#107—861no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—21no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429#97—431no—
430#97—431no—
431#97—861no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437#41—3441no—
438#41—3441no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—861no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×D4—21no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4C2×C22⋊D4311yescharacteristic
449C22×C4—21no—
450C22×C4—1721no—
451C22×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454Q16—81no—
455Q16—3441no—
456SD16—81no—
457SD16—3441no—
458SD16—3441no—
459SD16—1722no—
460SD16—1722no—
461D8—3441no—
462M16—862no—
463M16—1722no—
464M16—1721no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—1722no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4C2×C22⋊D4311yescharacteristic
490C4⋊C4C2×C22⋊D4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—21no—
500C42—41no—
501C42D4×D4311yescharacteristic
502C42#1062190011yescharacteristic
503C42C2×C22⋊D4311yescharacteristic
504C42C23×D4311yescharacteristic
505C23—21no—
506C23—1721no—
507C23#1306329711yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—1721no—
515Q8—1721no—
516D4—21no—
517D4—21no—
518D4—81no—
519D4—3441no—
520D4—3442no—
521D4—1721no—
522D4—1721no—
523D4—1721no—
524D4—1721no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—3442no—
538C2×C4—1721no—
539C2×C4#1306329711yescharacteristic
540C2×C4#1306329711yescharacteristic
541C2×C4#1306329711yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C22×C22⋊D4311yescharacteristic
544C2×C4C2×#1062190011yescharacteristic
545C8—41no—
546C8—41no—
547C8—432no—
548C8—861no—
549C8—861no—
550C8—861no—
551C8—1721no—
552C8—1721no—
553C8—1721no—
554C8—1721no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—3441no—
562C22—3441no—
563C22—3441no—
564C22C2×#1306329711yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—3441no—
575C4#135×D4311yescharacteristic
576C4#1458369611yescharacteristic
577C4#1458370211yescharacteristic
578C4#1458370711yescharacteristic
579C2—41no—
580C2—81no—
581C2—6881no—
582C2#1914404611yescharacteristic
583C2#1914427711yescharacteristic
584C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#19145567C2
hypercenter#3248D43
hypocenterC43#19252
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19145314C2semidirect
3. #19143600C2semidirect
4. #19134165C2semidirect
5. #19134147C2semidirect
6. #19134106C2semidirect
7. #19134062C2semidirect
8. #19134034C2semidirect
9. #19134016C2semidirect
10. #19133987C2semidirect
11. #19133945C2semidirect
12. #19133345C2semidirect
13. #19133260C2semidirect
14. #19133245C2semidirect
15. C43×#3248C2semidirect
287. #3248D43semidirect
359. C43#19252semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191455672
#191453142
#191436002
#191341652
#191341472
#191341062
#191340622
#191340342
#191340162
#191339872
#191339452
#191333452
#191332602
#191332452
C43×#32482
#1925243